A proof of any form requires logical reasoning. Logical reasoning ensures that the conclusions you reach are true-if the rest of the statements in the argument are true.
Logic
CONDITIONAL: If p then q or ( P => Q)
deductive reasoning/deduction: The process of drawing conclusions by using an argument. If then statements!
If a car is a corvette then it's a Chevrolet. This statement is a conditional statement.
In a conditional the part following the word if is the hypothesis. The part following the word then is the conclusion.
When you interchange the hypothesis and the conclusion of a conditional the new conditional is called a converse of the original conditional.
An "IF" "THEN" statement is called a "conditional statement"
All definitions can be interpreted "forward" and "backward"
If a car is a Chevrolet then the car is a Corvette.
IF-THEN TRANSITIVE PROPERTY
-Given: If A then B, and if B then C. -You can conclude: If A then C. Counterexample - an example which proves that a statement is false
Perpendicular: two lines that intersect to form a right angle.
perpendicular angle Biconditional Statement: a logical statement containing "If and only If".
a biconditional is equivalent to writing a conditional statement and its converse.
A biconditional statement can be true or false. To be true, both the conditional and its converse must be true. All definitions are biconditional statements.
Example: If cats freak, then mice frisk
If sirens shriek, then dogs howl
If dogs howl, then cats frisk
Solution: If sirens shriek, then dogs howl
If dogs howl, then cats freak
If cats freak, then mice frisk
Logic
CONDITIONAL: If p then q or ( P => Q)
deductive reasoning/deduction: The process of drawing conclusions by using an argument.
If then statements!
If a car is a corvette then it's a Chevrolet. This statement is a conditional statement.
In a conditional the part following the word if is the hypothesis. The part following the word then is the conclusion.
When you interchange the hypothesis and the conclusion of a conditional the new conditional is called a converse of the original conditional.
An "IF" "THEN" statement is called a "conditional statement"
- All definitions can be interpreted "forward" and "backward"
If a car is a Chevrolet then the car is a Corvette.IF-THEN TRANSITIVE PROPERTY
- Given: If A then B, and if B then C.
- You can conclude: If A then C.
Counterexample - an example which proves that a statement is false
Perpendicular: two lines that intersect to form a right angle.
Biconditional Statement: a logical statement containing "If and only If".
- a biconditional is equivalent to writing a conditional statement and its converse.
A biconditional statement can be true or false. To be true, both the conditional and its converse must be true. All definitions are biconditional statements.Example: If cats freak, then mice frisk
If sirens shriek, then dogs howl
If dogs howl, then cats frisk
Solution: If sirens shriek, then dogs howl
If dogs howl, then cats freak
If cats freak, then mice frisk